In a DC circuit with a capacitor, as time passes after applying voltage, the charging current does what?

• A. Increases
• B. Fluctuates
• C. Decreases to zero
• D. Reverses sign

Answer: (C)

When a DC source charges a capacitor, the current changes as the capacitor charges. At the moment you connect the circuit, the uncharged capacitor looks like a short, so the current is at its maximum (set by the supply and the series resistance). As the capacitor stores more charge, its voltage rises, which reduces the voltage drop across the resistor. That causes the charging current to fall. The capacitor voltage approaches the supply voltage, and the current continues to decrease until it becomes essentially zero, at which point the capacitor is fully charged and the circuit reaches steady state.

In math terms, the current decays exponentially with time constant RC, starting at V_s/R and approaching zero as time goes on. The voltage across the capacitor rises toward V_s in the same exponential manner. Reversing the current would only happen if the source polarity changed or the capacitor discharged through another path; with a fixed DC source, the charging current does not reverse.